(4w-3)(2+w)=0

Solution for (4w-3)(2+w)=0 equation:

Simplifying
(4w + -3)(2 + w) = 0

Reorder the terms:
(-3 + 4w)(2 + w) = 0

Multiply (-3 + 4w) * (2 + w)
(-3(2 + w) + 4w * (2 + w)) = 0
((2 * -3 + w * -3) + 4w * (2 + w)) = 0
((-6 + -3w) + 4w * (2 + w)) = 0
(-6 + -3w + (2 * 4w + w * 4w)) = 0
(-6 + -3w + (8w + 4w2)) = 0

Combine like terms: -3w + 8w = 5w
(-6 + 5w + 4w2) = 0

Solving
-6 + 5w + 4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-2 + -1w)(3 + -4w) = 0

Subproblem 1
Set the factor '(-2 + -1w)' equal to zero and attempt to solve:

Simplifying
-2 + -1w = 0

Solving
-2 + -1w = 0

Move all terms containing w to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -1w = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1w = 0 + 2
-1w = 0 + 2

Combine like terms: 0 + 2 = 2
-1w = 2

Divide each side by '-1'.
w = -2

Simplifying
w = -2
Subproblem 2
Set the factor '(3 + -4w)' equal to zero and attempt to solve:

Simplifying
3 + -4w = 0

Solving
3 + -4w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -4w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4w = 0 + -3
-4w = 0 + -3

Combine like terms: 0 + -3 = -3
-4w = -3

Divide each side by '-4'.
w = 0.75

Simplifying
w = 0.75
Solution
w = {-2, 0.75}